The underlying geometry of cognitive maps could take a number of forms. At one extreme, spatial knowledge might have a Euclidean structure that preserves metric distances and angles (Gallistel, 1990). At the other, it might have a topological graph structure that only preserves the connectivity between known places. We introduce two “wormholes” that rotate and/or translate a walker between remote places in a virtual hedge maze, making it non-Euclidean. A Euclidean control maze has the same layout and graph structure, but no wormholes. Previous research (Rothman & Warren, VSS 2006) found that participants learn the wormhole maze as quickly as the Euclidean maze, and take advantage of the wormholes, but do not even notice the inconsistent Euclidean structure. Here we probe their spatial knowledge by asking them to take novel shortcuts between learned places. In the experiment, participants walked in an immersive virtual environment (12m × 12m) while wearing a head-mounted display (60° × 40° FOV) with a sonic/inertial tracking system (50–70ms latency). On learning trials, they explored the environment, visiting all 8 objects, and then were trained to a criterion of two successful trials walking from a Home location to each object. In the test phase, participants walked from Home to object A, the entire maze was removed, and they then took a direct shortcut to the remembered location of object B. If participants acquired a metric cognitive map, they should walk to definite locations - either to the initial object positions or their post-wormhole positions (e.g. rotated by 90°). If instead they acquired a topological graph, shortcuts should be highly variable. The results will provide insight into the nature and consistency of the spatial knowledge that is learned for navigation.